Mesh Generation
Including coverage of mesh modification tools, evaluation criteria, optimization, and more, this book provides a comprehensive survey of the different algorithms and data structures for triangulation and meshing construction.
TABLE OF CONTENTS Mesh Generation
Symbols and Notations
Notations
| d | refers to the spatial dimension |
| | set of integers, set of reals |
| ? | refers to a closed geometric domain of |
| ?? | refers to the (discretized) boundary of ? |
| ?( ?) | refers to the boundary of ? |
| ?, ? | refers to a curve, a surface |
| ?, ? | refers to the parametrization of a curve, a surface |
| | refers to a triangulation or a mesh |
| | refers to a set of vertices |
| Const | refers to a constraint (a set of entities) |
| Conv( | refers to the convex hull of |
| ( ?, H) | refers to a control space |
| K | refers to a mesh element |
| S K, V K | refers to the surface area, the volume of element K |
| Q K | shape quality of mesh element K |
| d AB, d(A,B) | (Euclidean) distance between A and B |
| | Euclidean length of segment PQ |
| | (normalized) length of edge AB |
Symbols
| ? | gradient operator |
| | Hessian tensor |
| a | absolute value |
| ?. ? | integer part or restriction |
| ? ? | Euclidean length of a vector |
| [ a, b] | a closed interval |
| ? u, v ? | dot product of two vectors |
| (. ?.) | cross product of two vectors |
| t u | u transposed (also u 1) |
Abbreviations
| ALE | Arbitrary Lagrangian Eulerian |
| BRep, F-Rep | Boundary Representation, Function Representation |
| CAD | Computer Aided Design |
| CSG | Constructive Solid Geometry |
| MAT | Medial Axis Transform |
| FEM | Finite Element Method |
| PDE | Partial Derivative Equation |
| NURBS | Non Uniform Rational B-Splines |
| LIFO |
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